Open AccessMaslov theory for surface wave propagation on a laterally heterogeneous earth
Author(s) -
Tromp Jeroen,
Dahlen F. A.
Publication year - 1993
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1993.tb01203.x
Subject(s) - space (punctuation) , surface (topology) , tensor (intrinsic definition) , phase space , representation (politics) , manifold (fluid mechanics) , covariant transformation , momentum (technical analysis) , physics , surface wave , mathematical analysis , classical mechanics , mathematics , geometry , quantum mechanics , optics , mechanical engineering , linguistics , finance , politics , political science , law , economics , philosophy , engineering
SUMMARY The usual JWKB ray‐theoretical description of Love and Rayleigh surface wave propagation on a smooth, laterally heterogeneous earth model breaks down in the vicinity of caustics, near the source and its antipode. In this paper we use Maslov theory to obtain a representation of the wavefield that is valid everywhere, even in the presence of caustics. The surface wave trajectories lie on a 3‐D manifold in 4‐D phase space ( θ, φ, k θ , k φ ), where θ is the colatitude, φ is the longitude, and k θ and k φ are the covariant components of the wave vector. There are no caustics in phase space; it is only when the rays are projected onto configuration space (θ, φ), the mixed spaces ( k θ , φ) and (θ, k φ ), or momentum space ( k θ , k φ ), that caustics occur. The essential strategy is to employ a mixed‐space or momentum‐space representation in the vicinity of configuration‐space caustics, where the (θ, φ) representation fails. By this means we obtain a uniformly valid Green's tensor and an explicit asymptotic expression for the surface wave response to a moment tensor source.